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Chapter 4: Problem 97

Oliver has a mass of \(76.2 \mathrm{kg} .\) He is riding in an elevator that has a downward acceleration of \(1.37 \mathrm{m} / \mathrm{s}^{2} .\) With what magnitude force does the elevator floor push upward on Oliver?

Short Answer

Expert verified
Answer: The magnitude of the force exerted by the elevator floor on Oliver is 642.888 N.

Step by step solution

01

1. Identify Knowns and Unknowns

We have the following information given: - Oliver's mass (m): \(76.2 \mathrm{kg}\) - The elevator's downward acceleration (a): \(1.37 \mathrm{m} / \mathrm{s}^{2}\) - Gravitational acceleration (g): \(9.81 \mathrm{m} / \mathrm{s}^{2}\) Our objective is to determine the force exerted by the elevator floor on Oliver.
02

2. Express Newton's Second Law of Motion

The force exerted by the elevator on Oliver, denoted as F, is given by Newton's second law of motion, which states that the force is equal to the mass multiplied by the acceleration. F = m × a However, we need to consider the effects of gravity on Oliver. The gravitational force acting on him can be calculated by: Gravitational Force = m × g Thus, the net force acting on Oliver inside the elevator is the difference between gravitational force and force exerted by the elevator floor.
03

3. Calculate the Gravitational Force

Calculate Oliver's gravitational force using the given mass and gravitational acceleration: Gravitational Force = m × g = 76.2 kg × 9.81 m/s² = 747.282 N (Keep the units to ensure consistency in the final calculation.)
04

4. Calculate the Net Force Acting on Oliver

Now, we'll calculate the net force acting on Oliver using his mass and the elevator's acceleration: Net Force = m × a = 76.2 kg × 1.37 m/s² = 104.394 N
05

5. Calculate the Force Exerted by the Elevator Floor

Since the net force acting on Oliver is the difference between the gravitational force and the force exerted by the elevator floor (F), we can solve for the force exerted by the elevator floor: F = Gravitational Force - Net Force = 747.282 N - 104.394 N = 642.888 N The elevator floor pushes upward on Oliver with a magnitude force of 642.888 N.

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